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Binaries consisting of a pulsar and a black hole (BH) are a holy grail of astrophysics, both for their significance for stellar evolution and for their potential application as probes of strong gravity. In spite of extensive surveys of our Galaxy and its system of globular clusters, no pulsar–black hole (PSR–BH) binary has been found to date. Clues as to where such systems might exist are therefore important. We show that if the central parsec around Sgr A★ harbours a cluster of ∼25 000 stellar BHs (as predicted by mass-segregation arguments) and if it is also rich in recycled pulsar binaries...

Binaries consisting of a pulsar and a black hole (BH) are a holy grail of astrophysics, both for their significance for stellar evolution and for their potential application as probes of strong gravity. In spite of extensive surveys of our Galaxy and its system of globular clusters, no pulsar–black hole (PSR–BH) binary has been found to date. Clues as to where such systems might exist are therefore important. We show that if the central parsec around Sgr A★ harbours a cluster of ∼25 000 stellar BHs (as predicted by mass-segregation arguments) and if it is also rich in recycled pulsar binaries (by analogy with globular clusters), then three-body exchange interactions should produce PSR–BHs in the Galactic Centre. Simple estimates of the formation rate and survival time of these binaries suggest that a few PSR–BHs should be present in the central parsec today. The proposed formation mechanism makes unique predictions for the PSR–BH properties: (1) the binary would reside within ∼1 pc of Sgr A★; (2) the pulsar would be recycled, with a period of ∼1 to a few tens of milliseconds, and a low magnetic field B≲ 1010 G; (3) the binary would have high eccentricity, e∼ 0.8, but with a large scatter and (4) the binary would be relatively wide, with semimajor axis ab∼ 0.1 −≳3 au. The potential discovery of a PSR–BH binary therefore provides a strong motivation for deep, high-frequency radio searches for recycled pulsars towards the Galactic Centre.